Cardiovascular Engineering and Technology

, Volume 9, Issue 4, pp 582–596 | Cite as

Uncertainty Quantification for Non-invasive Assessment of Pressure Drop Across a Coarctation of the Aorta Using CFD

  • Jan BrüningEmail author
  • Florian Hellmeier
  • Pavlo Yevtushenko
  • Titus Kühne
  • Leonid Goubergrits



Numerical assessment of the pressure drop across an aortic coarctation using CFD is a promising approach to replace invasive catheter-based measurements. The aim of this study was to investigate and quantify the uncertainty of numerical calculation of the pressure drop introduced during two essential steps of medical image processing: segmentation of the patient-specific geometry and measurement of patient-specific flow rates from 4D-flow-MRI.


Based on the baseline segmentation, geometries with different stenosis diameters were generated for a sample of ten patients. The pressure drop generated by these geometries was calculated for different volume flow rates using computational fluid dynamics. Based on these simulations, a second order polynomial fit was calculated. Based on these polynomial fits an uncertainty of pressure drop calculation was quantified.


The calculated pressure drop values varied strongly between the patients. In four patients, pressure drops above and below the clinical threshold of 20 mmHg were found. The median standard deviation of the pressure drop was 2.3 mmHg. The sensitivity of the pressure drop toward changes in the volume flow rate or the stenosis geometry varied between patients.


The uncertainty of numerical pressure drop calculation introduced by uncertainties during image segmentation and measurement of volume flow rates was comparable to the uncertainty of pressure drop measurements using invasive catheterization. However, in some patients this uncertainty would have led to different treatment decision. Therefore, patient-specific uncertainty assessment might help to better understand the reliability of a numerically calculated biomarker as the pressure drop across an aortic coarctation.


Coarctation of the aorta Computational fluid dynamics Image-based modeling Hemodynamics Uncertainty analysis Non-invasive diagnosis 


Conflict of interest

The authors declare that they has no conflict of interest.

Ethical Approval

All procedures performed in studies involving human participants were in accordance with the ethical standards of the institutional and/or national research committee and with the 1964 Helsinki declaration and its later amendments or comparable ethical standards.

Informed Consent

Informed consent was obtained from all individual participants and/or their guardians included in the study.


This work was funded by the German Research Foundation (IDs GO1967/6-1 and KU1329/10-1) and the European Commission (ID 611232).


  1. 1.
    Abraham, F., M. Behr, and M. Henkenschloss. Shape optimization in steady blood flow: a numerical study of non-Newtonian effects. Comput. Methods Biomech. Biomed. Eng. 8(2):127–137, 2005.CrossRefGoogle Scholar
  2. 2.
    Andersson, M., J. Lantz, T. Ebbers, and M. Karlsson. Quantitative assessment of turbulence and flow eccentricity in an aortic coarctation: impact of virtual interventions. Cardiovasc. Eng. Technol. 6(3):281–293, 2015.CrossRefGoogle Scholar
  3. 3.
    Bermejo, J., F. Alfonso, and X. Bosch. Imaging techniques in cardiovascular medicine. Rev. Esp. Cardiol. 56:193–194, 2003.Google Scholar
  4. 4.
    Boccadifuoco, A., A. Mariotti, S. Celi, N. Martini, M. V. Salvetti. Impact of uncertainties in outflow boundary conditions on the predictions of hemodynamic simulations of ascending thoracic aortic aneurysms. Comput. Fluids. 165:96–115. ECCOMAS Congress 2016 Proceedings, 2018.Google Scholar
  5. 5.
    Boccadifuoco A, Mariotti A, Celi S, Martini N, Salvetti MV. Uncertainty quantification in numerical simulations of the flow in thoracic aortic aneurysms.Google Scholar
  6. 6.
    Botar, C. C., Á. Á. Tóth, O. R. Klisurić, D. D. Nićiforović, V. A. Vučaj Ćirilović, and V. E. Till. Dynamic simulation and doppler ultrasonography validation of blood flow behavior in abdominal aortic aneurysm. Phys. Med. 37:1–8, 2017.CrossRefGoogle Scholar
  7. 7.
    Bozzi, S., U. Morbiducci, D. Gallo, R. Ponzini, G. Rizzo, C. Bignardi, and G. Passoni. Uncertainty propagation of phase contrast-MRI derived inlet boundary conditions in computational hemodynamics models of thoracic aorta. Comput. Methods Biomech. Biomed. Eng. 20(10):1104–1112, 2017.CrossRefGoogle Scholar
  8. 8.
    Bozzi, S., U. Morbiducci, D. Gallo, R. Ponzini, G. Rizzo, C. Bignardi, and G. Passoni. Uncertainty propagation of phase contrast-MRI derived inlet boundary conditions in computational hemodynamics models of thoracic aorta. Comput. Methods Biomech. Biomed. Eng. 10:1104–1112, 2017.CrossRefGoogle Scholar
  9. 9.
    Bruening, J., F. Hellmeier, P. Yevtushenko, M. Kelm, S. Nordmeyer, S. H. Sündermann, T. Kuehne, and L. Goubergrits. Impact of patient-specific LVOT inflow profiles on aortic valve prosthesis and ascending aorta hemodynamics. J. Comput. Sci. 24:91–100, 2018.CrossRefGoogle Scholar
  10. 10.
    Canniffe, C., P. Ou, K. Walsh, D. Bonnet, and D. Celermajer. Hypertension after repair of aortic coarctation—a systematic review. Int. J. Cardiol. 167(6):2456–2461, 2013.CrossRefGoogle Scholar
  11. 11.
    Celi, S., and S. Berti. Biomechanics and FE modelling of aneurysm: review and advances in computational models, aneurysm. IntechOpen 2012. Scholar
  12. 12.
    Celi, S., and S. Berti. Three-dimensional sensitivity assessment of thoracic aortic aneurysm wall stress: a probabilistic finite-element study. Eur. J. Cardio-Thorac. Surg. 45:467–475, 2014.CrossRefGoogle Scholar
  13. 13.
    Celi, S., N. Martini, L. E. Pastormerlo, V. Positano, and S. Berti. Multimodality imaging for interventional cardiology. Curr. Pharm. Des. 23(22):3285–3300, 2017.CrossRefGoogle Scholar
  14. 14.
    Douglas, P. S., B. De Bruyne, G. Pontone, M. R. Patel, B. L. Norgaard, R. A. Byrne, N. Curzen, I. Purcell, M. Gutberlet, G. Rioufol, U. Hink, H. W. Schuchlenz, G. Feuchtner, M. Gilard, D. Andreini, J. M. Jensen, M. Hadamitzky, K. Chiswell, D. Cyr, A. Wilk, F. Wang, C. Rogers, and M. A. Hlatky. 1-year outcomes of FFRCT-guided care in patients with suspected coronary disease: the PLATFORM study. J. Am. Coll. Cardiol. 68(5):435–445, 2016.CrossRefGoogle Scholar
  15. 15.
    Eck, V. G., W. P. Donders, J. Sturdy, J. Feinberg, T. Delhaas, L. R. Hellevik, and W. Huberts. A guide to uncertainty quantification and sensitivity analysis for cardiovascular applications. Int. J. Numer. Method Biomed. Eng. 21(8):e02755, 2016.MathSciNetCrossRefGoogle Scholar
  16. 16.
    Eck, V. G., J. Sturdy, and L. R. Hellevik. Effects of arterial wall models and measurement uncertainties on cardiovascu-lar model predictions. J. Biomech. 50:188–194, 2017.CrossRefGoogle Scholar
  17. 17.
    Friman, O., A. Hennemuth, A. Harloff, J. Bock, M. Markl, and H. O. Peitgen. Probabilistic 4D blood flow tracking and uncertainty estimation. Med. Image Anal. 15(5):720–728, 2011.CrossRefGoogle Scholar
  18. 18.
    Gallo, D., G. De Santis, F. Negri, D. Tresoldi, R. Ponzini, D. Massai, M. A. Deriu, P. Segers, B. Verhegghe, G. Rizzo, and U. Morbiducci. On the use of in vivo measured flow rates as boundary conditions for image-based hemodynamic models of the human aorta: implications for indicators of abnormal flow. Ann. Biomed. Eng. 40(3):729–741, 2012.CrossRefGoogle Scholar
  19. 19.
    Goubergrits, L., R. Mevert, P. Yevtushenko, J. Schaller, U. Kertzscher, S. Meier, S. Schubert, E. Riesenkampff, and T. Kuehne. The impact of MRI-based inflow for the hemodynamic evaluation of aortic coarctation. Ann. Biomed. Eng. 41:2575–2587, 2013.CrossRefGoogle Scholar
  20. 20.
    Goubergrits, L., E. Riesenkampff, P. Yevtushenko, J. Schaller, U. Kertzscher, F. Berger, and T. Kuehne. Is MRI-based CFD able to improve clinical treatment of coarctations of aorta? Ann. Biomed. Eng. 43(1):168–176, 2015.CrossRefGoogle Scholar
  21. 21.
    Goubergrits, L., E. Riesenkampff, P. Yevtushenko, J. Schaller, U. Kertzscher, A. Hennemuth, F. Berger, S. Schubert, and T. Kuehne. MRI-based computational fluid dynamics for diagnosis and treatment prediction: clinical validation study in patients with coarctation of aorta. J. Magn. Reson. Imaging. 41(4):909–916, 2015.CrossRefGoogle Scholar
  22. 22.
    Hellmeier, F., S. Nordmeyer, P. Yevtushenko, J. Bruening, F. Berger, T. Kuehne, L. Goubergrits, and M. Kelm. Hemodynamic evaluation of a biological and mechanical aortic valve prosthesis using patient-specific MRI-based CFD. Artif. Org. 42(1):49–57, 2018.CrossRefGoogle Scholar
  23. 23.
    Huberts, W., K. Van Canneyt, P. Segers, S. Eloot, J. H. Tordoir, P. Verdonck, F. N. van de Vosse, and E. M. Bosboom. Experimental validation of a pulse wave propagation model for predicting hemodynamics after vascular access surgery. J. Biomech. 45(9):1684–1691, 2012.CrossRefGoogle Scholar
  24. 24.
    International Electrotechnical Commission Standard: IEC 60601-2-34:2011. Medical electrical equipment—Part 2–34: Particular requirements for the basic safety and essential performance of invasive blood pressure monitoring equipment, 2011.Google Scholar
  25. 25.
    Isaaz, K., J. F. Bruntz, A. Da Costa, D. Winninger, A. Cerisier, C. de Chillou, N. Sadoul, M. Lamaud, G. Ethevenot, and E. Aliot. Noninvasive quantitation of blood flow turbulence in patients with aortic valve disease using online digital computer analysis of doppler velocity data. J. Am. Soc. Echocardiogr. 16(9):965–974, 2003.CrossRefGoogle Scholar
  26. 26.
    Itu, L., P. Sharma, and K. Ralovich. Non-invasive hemodynamic assessment of aortic coarctation: validation with in vivo measurements. Ann. Biomed. Eng. 41:669–681, 2013.CrossRefGoogle Scholar
  27. 27.
    Jager, M. D., J. C. Aldag, and G. G. Deshpande. A presedation fluid bolus does not decrease the incidence of propofol-induced hypotension in pediatric patients. Hosp. Pediatr. 5(2):85–91, 2015.CrossRefGoogle Scholar
  28. 28.
    Karimi, S., M. Dabagh, P. Vasava, M. Dadvar, B. Dabir, and B. Jalali. Effect of rheological models on the hemodynamics within human aorta: CFD study on CT image-based geometry. J. Non-Newton. Fluid Mech. 207:42–52, 2004.CrossRefGoogle Scholar
  29. 29.
    Kousera, C. A., N. B. Wood, W. A. Seed, R. Torii, D. O’Regan, and X. Y. Xu. A numerical study of aortic flow stability and comparison with in vivo flow measurements. J. Biomech. Eng. 135(1):011003, 2013.CrossRefGoogle Scholar
  30. 30.
    Kuprat, A., A. Khamayseh, D. George, and L. Larkey. Volume conserving smoothing for piecewise linear curves, surfaces and triple lines. J. Comput. Phys. 172:99–118, 2001.CrossRefzbMATHGoogle Scholar
  31. 31.
    Liu, X., Y. Fan, X. Deng, and F. Zhan. Effect of non-Newtonian and pulsatile blood flow on mass transport in the human aorta. J. Biomech. Eng. 44:1123–1131, 2011.CrossRefGoogle Scholar
  32. 32.
    Melero-Ferrer, J. L., R. López-Vilella, H. Morillas-Climent, J. Sanz-Sánchez, I. J. Sánchez-Lázaro, L. Almenar-Bonet, and L. Martínez-Dolz. Novel imaging techniques for heart failure. Card. Fail. Rev. 2(1):27–34, 2016.CrossRefGoogle Scholar
  33. 33.
    Mirzaee, H., T. Henn, M. J. Krause, L. Goubergrits, C. Schumann, M. Neugebauer, T. Kuehne, T. Preusser, and A. Hennemuth. MRI-based computational hemodynamics in patients with aortic coarctation using the lattice Boltzmann methods: clinical validation study. J. Magn. Reson. Imaging. 45(1):139–146, 2017.CrossRefGoogle Scholar
  34. 34.
    Morbiducci, U., R. Ponzini, D. Gallo, C. Bignardi, and G. Rizzo. Inflow boundary conditions for image-based computational hemodynamics: impact of idealized versus measured velocity profiles in the human aorta. J. Biomech. 46(1):102–109, 2013.CrossRefGoogle Scholar
  35. 35.
    Murray, C. D. The physiological principle of minimum work. I. The vascular system and the cost of blood volume. Proc. Natl. Acad. Sci. 12(3):207–214, 1926.CrossRefGoogle Scholar
  36. 36.
    Quarteroni, A., A. Veneziani, and C. Vergara. Geometric multiscale modeling of the cardiovascular system, between theory and practice. Comput. Methods Appl. Mech. Eng. 302:193–252, 2016.MathSciNetCrossRefGoogle Scholar
  37. 37.
    Quicken, S., W. P. Donders, E. M. van Disseldorp, K. Gashi, B. M. Mees, F. N. van de Vosse, R. G. Lopata, T. Delhaas, and W. Huberts. Application of an adaptive polynomial chaos expansion on computationally expensive three-dimensional cardiovascular models for uncertainty quantification and sensitivity analysis. J. Biomech. Eng. 138(12):121010, 2016.CrossRefGoogle Scholar
  38. 38.
    Riesenkampff, E., J. F. Fernandes, S. Meier, L. Goubergrits, S. Kropf, S. Schubert, F. Berger, A. Hennemuth, and T. Kuehne. Pressure fields by flow-sensitive, 4D, velocity-encoded CMR in patients with aortic coarctation. JACC Cardiovasc. Imaging. 7(9):920–926, 2014.CrossRefGoogle Scholar
  39. 39.
    Sankaran, S., L. Grady, and C. A. Taylor. Impact of geometric uncertainty on hemodynamic simulations using ma-chine learning. Comput. Methods Appl. Mech. Eng. 297:167–190, 2015.CrossRefGoogle Scholar
  40. 40.
    Sankaran, S., and A. L. Marsden. A stochastic collocation method for uncertainty quantification and propagation in cardiovascular simulations. J. Biomech. Eng. 133(3):031001, 2011.CrossRefGoogle Scholar
  41. 41.
    Senko, I., A. Shatokhin, I. Bishnoi, Y. Yamada, R. Tanaka, D. Suyama, T. Kawase, and Y. Kato. Intraoperative rupture cerebral aneurysm and computational flow dynamics. Asian J. Neurosurg. 13(2):496–498, 2018.CrossRefGoogle Scholar
  42. 42.
    Tran, J. S., D. E. Schiavazzi, A. B. Ramachandra, A. M. Kahn, and A. L. Marsden. Automated tuning for parameter identification and uncertainty quantification in multi-scale coronary simulations. Comput. Fluids 142:128–138, 2017.MathSciNetCrossRefzbMATHGoogle Scholar
  43. 43.
    van Bakel, T. M. J., K. D. Lau, J. Hirsch-Romano, S. Trimarchi, A. L. Dorfman, and C. A. Figueroa. Patient-specific modeling of hemodynamics: supporting surgical planning in a fontan circulation correction. J. Cardiovasc. Transl. Res. 11(2):145–155, 2018.CrossRefGoogle Scholar
  44. 44.
    Warnes, C. A., et al. ACC/AHA 2008 guidelines for the management of adults with congenital heart disease: a report of the American College of Cardiology/American Heart Association Task Force on Practice Guidelines (writing committee to develop guidelines on the management of adults with congenital heart disease). Circulation 118(23):e714–e833, 2008.Google Scholar
  45. 45.
    Wyman, R. M., R. D. Safian, V. Portway, J. J. Skillman, R. G. McKay, and D. S. Baim. Current complications of diagnostic and therapeutic cardiac catheterization. J. Am. Coll. Cardiol. 12(6):1400–1406, 1988.CrossRefGoogle Scholar
  46. 46.
    Yevtushenko, P., F. Hellmeier, J. Brüning, T. Kuehne, and L. Goubergrits. Numerical investigation of the impact of branching vessel boundary conditions on aortic hemodynamics. Curr. Dir. Biomed. Eng. 3(2):321–324, 2017.Google Scholar
  47. 47.
    Zhu, Y., R. Chen, Y. H. Juan, H. Li, J. Wang, Z. Yu, and H. Liu. Clinical validation and assessment of aortic hemodynamics using computational fluid dynamics simulations from computed tomography angiography. Biomed. Eng. Online 17(1):53, 2018.CrossRefGoogle Scholar

Copyright information

© Biomedical Engineering Society 2018

Authors and Affiliations

  • Jan Brüning
    • 1
    Email author
  • Florian Hellmeier
    • 1
  • Pavlo Yevtushenko
    • 1
  • Titus Kühne
    • 1
    • 2
    • 3
  • Leonid Goubergrits
    • 1
  1. 1.Institute for Imaging Science and Computational Modelling in Cardiovascular MedicineCharité – Universitätsmedizin BerlinBerlinGermany
  2. 2.Department of Congenital Heart Disease - Unit of Cardiovascular ImagingGerman Heart Center BerlinBerlinGermany
  3. 3.DZHK (German Centre for Cardiovascular Research), Partner Site BerlinBerlinGermany

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